Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	8
1	61	8
2	141	8
3	347	8
4	792	8
5	5002	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
0.7b	(- (* (* z 2.0) z) (* y t))
19.9b	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
5×	`add-cube-cbrt`
3×	`pow1` `cbrt-undiv` `flip3--` `times-frac` `div-exp` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `diff-log` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 51

Calls

3 calls:

8.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
4.0ms	(- (* (* z 2.0) z) (* y t))
10.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
36.0ms	(- (* (* z 2.0) z) (* y t))
185.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

simplify46.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	318	564
1	1519	493
2	5002	493

prune149.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y)))))
0.7b	(- (* 2.0 (pow z 2)) (* t y))
4.3b	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
19.3b	(/ z (- (* 2.0 (pow z 2)) (* t y)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `times-frac` `add-cbrt-cube`
15×	`associate-r`
9×	`pow1`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r` `associate-/l`
2×	`sub-neg` `diff-log` `div-inv`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 88

Calls

4 calls:

2.0ms	(- x (* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y)))))
4.0ms	(- (* 2.0 (pow z 2)) (* t y))
10.0ms	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
6.0ms	(/ z (- (* 2.0 (pow z 2)) (* t y)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- x (* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y)))))
42.0ms	(- (* 2.0 (pow z 2)) (* t y))
185.0ms	(* (* y 2.0) (/ z (- (* 2.0 (pow z 2)) (* t y))))
51.0ms	(/ z (- (* 2.0 (pow z 2)) (* t y)))

simplify62.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	391	883
1	1978	774
2	5003	773

prune260.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
0.7b	(- (* (* z 2.0) z) (* y t))
4.6b	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
19.2b	(/ (- (* (* z 2.0) z) (* y t)) z)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `div-inv` `associate-/l*`
3×	`flip3--` `flip--`
2×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`div-sub` `associate-/r/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

10.0ms	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
4.0ms	(- (* (* z 2.0) z) (* y t))
8.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
7.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

series358.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
40.0ms	(- (* (* z 2.0) z) (* y t))
184.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
54.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

simplify68.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	472	1105
1	2263	993
2	5002	988

prune280.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z)))))
4.6b	(/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z))))
5.1b	(/ (* t y) z)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
20×	`add-cbrt-cube`
8×	`div-exp` `prod-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`cbrt-undiv`
5×	`add-cube-cbrt` `cbrt-unprod` `add-log-exp`
4×	`times-frac` `associate-/r*`
3×	`pow1`
2×	`flip3--` `frac-2neg` `1-exp` `associate-r/` `clear-num` `associate-/r/` `flip--` `div-inv` `associate-/l`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 60

Calls

3 calls:

8.0ms	(- x (/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z)))))
9.0ms	(/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z))))
5.0ms	(/ (* t y) z)

series259.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(- x (/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z)))))
172.0ms	(/ (* y 2.0) (* 1 (- (* 2.0 z) (/ (* t y) z))))
19.0ms	(/ (* t y) z)

simplify47.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	519
1	1869	433
2	5001	433

prune137.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes92.0ms

Accuracy

-14.3% (2.1b remaining)

Error of 2.7b against oracle of 0.5b and baseline of 2.4b

bsearch127.0ms

Steps

Iters	Range		Point
10	1.6480282302546184e+245	1.7935496845449555e+258	1.7509518152818834e+246
10	8.734071036478518e+160	1.6074914794613563e+177	6.4129800116043025e+168

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	16
1	42	16
2	42	16

end0.0ms

sample538.0ms

Algorithm

intervals

Results

327.0ms

8000×

body

valid